Solve the system using matrices (row operations)

Question

{ 6x+5y=62

   5x-6y=-50

 

x=?

y=?

Answer 1

The first operation should be to get one of your coefficients to be equal to the negative of one from the other equation(same variable).

so you have a 5x and a 6x. to go from 5->6 you multiply by 6/5. Its always a ratio of the two, where the number your going to is in the numerator and the number your coming from is in the denominator.

Now you multiply the whole equation containing 5x by that fraction

(6/5)*(5x-6y=-50)

6x-36*y/5=-60

Now the coefficients match between the two equation but we want the negative so when we add the equations they will cancel. So we just multiply everything by (-1) or flip the sign

-6x+36*y/5=60

And add them together

-6x+36*y/5=60   +

6x+5y=62           

0*x+(36/5+5)y=112

combine the fractions over a common denominator

(36/5+25/5)y=112

(61/5)y=112

Isolate the y by multiplying the inverse of its coefficient 

(5/61)*(61/5)y=(5/61)*112

y=5*112/61

y=5*(2/1)

y=10

Now that you have y just plug it back into any equation with both y and x.

5x-6y=-50

5x-6(10)=-50

5x-60=-50

5x=10

x=2

 

The solution you get is the intersection of the two equations. These equations have two variables which makes them lines. If you graph both these lines they will intersect at (2,10) or (x=2,y=10) as seen in the graph below 

http://www4b.wolframalpha.com/Calculate/MSP/MSP372321g3e8cg8be38h0g00003g3fead74gf4dd67?MSPStoreType=image/gif&s=53&w=411.&h=292.&cdf=RangeControl

 

Answer 2

6x+5y=62

5x-6y=-50

 

Writing in matrix form

 

6.   5.   62

5.  -6.   -50

 

Multiplying the first row 5 & second row by 6

 

30.    25.      310

30.    -36      -300

 

Subtracting second row from first

 

30.    25     310

0.      61.    610

 

Dividing the second row by 61

 

30.    25.     310

0.        1.     10

 

So,that gives y =10

 

Substitute back

 

You get

 

x= 2

 

Substitute back and verify your answer

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